Confidence interval for a 2-group ratio of standard deviations

Source: R/statpsych1.R

Computes a robust confidence interval for a ratio of population standard deviations in a 2-group design. This function is a modification of the confidence interval proposed by Bonett (2006). The original Bonett method used a pooled kurtosis estimate in the standard error that assumed equal variances, which limited the confidence interval's use to tests of equal population variances and equivalence tests. This function uses a pooled kurtosis estimate that does not assume equal variances and provides a useful confidence interval for a ratio of standard deviations under general conditions. This function requires of minimum sample size of four per group but sample sizes of at least 10 per group are recommended.

ci.ratio.sd2(alpha, y1, y2)

Arguments

alpha

alpha level for 1-alpha confidence

y1

vector of scores for group 1

y2

vector of scores for group 2

Value

Returns a 1-row matrix. The columns are:

  • SD1 - estimated SD for group 1

  • SD2 - estimated SD for group 2

  • SD1/SD2 - estimate of SD ratio

  • LL - lower limit of the confidence interval

  • UL - upper limit of the confidence interval

References

Bonett DG (2006). “Robust confidence interval for a ratio of standard deviations.” Applied Psychological Measurement, 30(5), 432--439. ISSN 0146-6216, doi:10.1177/0146621605279551 .

Examples

y1 <- c(32, 39, 26, 35, 43, 27, 40, 37, 34, 29)
y2 <- c(36, 44, 47, 42, 49, 39, 46, 31, 33, 48)
ci.ratio.sd2(.05, y1, y2)
#>       SD1      SD2   SD1/SD2       LL       UL
#>  5.711587 6.450667 0.8854257 0.486279 1.728396

# Should return:
#      SD1      SD2    SD1/SD2       LL       UL
# 5.711587 6.450667  0.8854257 0.486279 1.728396